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Physica 147B (1987) 311-315 North-Holland, Amsterdam
STUDY OF S E C O N D A R Y EMISSION
1/f NOISE
P. F A N G and A. VAN D E R Z I E L Electrical Engineering Department, University of Minnesota, Minneapolis, MN 55455, USA Received 25 May 1987 Revised manuscript received 4 August 1987
The secondary emission 1/f noise observed by Schwantes and Van der Ziel has been investigated in more detail. The new experiments were prompted by Van der Ziel's application of Handel's theory to Schwantes's 1960 secondary emission noise data. To that end we measured the spectrum Sl~(f ) versus (Va - Va)3/2 at constant current I a and constant 8 and the noise spectrum versus I,/52 at constant voltage (V, - Va) both for a large resistance Re in the cathode lead. The results show good agreement with Handel's prediction, i.e. Handel's expression for the Hooge parameter a H is here verified. We finally discuss the meaning of these results and show that the Bremsstrahlung hypothesis can explain most of the data.
and daa is the distance from dynode to anode. Substituting all of these into (1), we can write:
1. Introduction
The experiments were made on Philips EFP60 secondary emission tubes. Secondary emission 1/f noise in this kind of tube was observed by Schwantes and Van der Ziel [1] in 1960, but the quantum 1 / f noise behavior could not be investigated, since Handel's theory was not yet developed. Recently Van der Ziel [2] formulated Handel's prediction for the value of the Hooge parameter a H for these tubes, derived the formula 4 a 0 82 ( Av2'~ eI~ 2 Sla(f) = ~ \ - - ~ - / f--~da = 4KTgnsgma
(1)
and showed that eq. (1) could explain the experimental data (see below). H e r e Sl~(f ) is the secondary emission 1/f noise current spectrum, a 0 is the fine structure constant for electrons, Av is the velocity change of the secondary electrons along the electron path from dynode to anode, I a is the anode current, g ~ = OIa/3Va is the transconductance, rda is the transit time from the dynode to the anode, and 3 is the secondary emission multiplication factor. In our case,
Sla ( f ) = const.Ia 62(Va - Vd)3'2 ,
where the (Va - V o ) 3/2 term corresponds to the Av 3 term; here dW z comes from the acceleration process operating on the secondary electron and Av comes from the transit time of the carriers. Therefore, one can expect that both Sly(f)~ ( V a - V d ) 3/2 at constant 8 and I a and Sla(f )/ (82Ia) at constant (Va - V d ) should be independent of bias. Before discussing the measurements, we investigate the background of eq. (1). The Hooge equation [3] Sla ( f )
12a
aH
- fNcu
(2)
defines the Hooge parameter a n both theoretically and experimentally; Neff = Iaz/e is the effective number of carriers. Substituting for Noff yields
ela Sj~(f) = a H f,rda
Av2= __2e(Va --Vd )
(lb)
(2a)
m
2dd~ 2daa ~'d~- (Av) -- (2e/m)(V a - V u ) 1/2
(la)
so that a H can be evaluated by measuring Sla(f); the transit time za~ can be estimated with an
0378-4363 / 87 / $03.50 t~ Elsevier Science Publishers B .V. (North-Holland Physics Publishing Division)
312
P. Fang and A. van der Ziel / Study of secondary emission 1/f noise
accuracy of +-(20-30)%, caused by the inaccuracy in dda. Next Handel's equation [4] is introduced as modified by Van der Ziel: 4a { AV2'~ 4% AV2 an = ~-~\--~-'] = -~-w 32 5C
(2b)
so that eq. (1) follows from eq. (2a) by substituting (2b) into (2a). Here a = %32 is the fine structure constant for charge conglomerates q = 6e and % = 1/137 is the fine structure constant for electrons. Eq. (2b) expresses the fact that, since the charge conglomerates = 6e move as a unit, they also generate Bremsstrahlung as a unit. The experimental value of a H is defined in eq. (2a), whereas the theoretical value of ~n is defined by eq. (2b). They are independent of each other, but since both go back to eq. (2), they deal with the same parameter. Hence a comparison between theory and experiment is both possible and meaningful.
tion 1 / f noise, respectively. The conductance gx was introduced so that the uncorrelated noise generated by the cathode is represented by an equivalent noise emf eg at the grid, a noise current generator gxeg between screen grid and dynode, and by a noise current generator 6g x between dynode and anode [1]. If we use the same bias circuit as above, except that now the screen grid is connected to the cathode for ac, we have: Rr,' = ( 1 +
g x ) 2Rnt + Rnp + (1 + gmpRc)2Rns , gmp
(4)
R~c= ( 1 + gmp gx ~2 / R .t + R n p
(5)
and, since we measured that R'.¢ = R.¢, it follows from (3) and (5) that Rnt =
(1 -t- ~rnp _ , ?R / nt "4- Rnp ;
this means gx/gmp and Rnp are negligible. Then (2) and (4) can be written: 2. Noise measurements
Rna = Rnt + (1 + gmtRc)2Rns The measurement configurations and the equivalent circuit can be found in ref. [1]. The principles of measurements in our experiments are the same as in ref. [1], and i.e. a large resistance Rc in the cathode lead provides feedback and so reduces the cathode 1 / f noise. If screen grid and dynode are both a.c. grounded we have for the noise resistance Rna and Rnc with feedback ena ____[1 + (gg___~_Xomp)(l+gmtec)]zRnt +(1 + gmtnc)2(Rn~ + R.p)
(3)
and R.c = R . , ,
(3a)
where R.¢ is measured at the cathode. Rnt, R,s, R.p are the noise resistances of the cathode 1 / f noise, secondary emission 1/f noise, and parti-
(screen grid connected to ground), 2 R~ = Rat + (1 + gmpRc) Rr,s (screen grid connected to cathode), R.s = (R.a - Rnt)/(1 + gmtR¢) 2 = ( R " - Rnt)/(1 + gmpRc) 2 . Using this method, Schwantes and Van der Ziel found that Rns at 10Hz was 0 . 4 6 M ~ , at the appropriate bias. Van der Ziel [2] found, in turn, that this result was in very good agreement with eq. (1), if he took for dda the plausible value of 0.50cm, but did not use any other adjustable parameters. The value of 0.50cm was chosen from early memory of the tube design and might be off by 20-30%. We first repeated the experiment under the same condition. Then we went one step further
P. Fang and A. van der Ziel / Study of secondary emission 1/f noise
to measure the functional dependence of the noise spectra on voltage, current and 6. In the experiments of S i . ( f ) versus (V~- Vo)3j2, we kept I~ and 6 constant and changed ( V ~ - lid) from 50 V to 125 V. Two devices were measured. Then we measured Sl~(f ) versus 82I, by keeping V~ - V a = 125 V and changing 6 and 1 by changing V2. The experimental conditions and results are shown in tables I-IV. To make sure that the secondary emission noise in our experiments had a 1/f noise spectrum, the spectra Sza(f ) versus Table I E F P 6 0 , d e v i c e # 1, d e t e r m i n a t i o n of
Sta(f)/(Va - lid) ~2.
frequency were measured. The results shown in fig. 1 give I / f noise. Figs. 2 - 4 give St~(f)/(V a )3/2, : Sl~(f)/(62ia) and S,.(f)/[(V aV~)3/26 I~], respectively for each of the two tubes. From the data we can clearly see that S~(f)/ (Va - Vd)3/2 and Sta(f)/(62Ia) are independent of bias within experimental error as the theory requires. Furthermore, we had evaluated Sl~(f ) / [(Va - Vd)3/2Ia 32] based on our data and can now conclude from this that for each tube it is in-
E x p e r i m e n t a l c o n d i t i o n s : f = 10 Hz, I~ = 10.0 m A , 8 = 3.6
( V a - Vd)(V )
(V, - I'd) 3/2
Sl~(f)(A2/nz)
Sla(f)/(V a Vd) 3/2
50 75 100 125
0.354 0.650 1.000 1.400
0.48 1.06 1.56 2.32
1.34 1.63 1.56 1.66 A v e . 1.55
x x x ×
103 103 103 103
Table II E F P 6 0 , d e v i c e ~ 1, d e t e r m i n a t i o n of
St~(f )/3 21,.
× x x ×
- -
10 -18 10 -18 10 -18 10 -18
× x × × ×
10 -21 10 Zl 10 zl 10 21 10 -21 -+ 0.09 x 10 -zl
E x p e r i m e n t a l c o n d i t i o n s : f = 10 Hz, V~ - V~ = 125 V
V2(V )
S~(f)(AZ/Hz)
3
la(mA)
82/~(mA)
Sta/6Zl.
250 225 200 175
2.3 9.4 2.7 1.5
3.60 3.04 2.43 1.97
10.00 5.88 2.94 1.44
129.60 54.30 17.40 5.88
1.77 1.73 1.56 2.60 A v e . 1.92
× × × ×
10 -13 10 -19 10 -19 10 -19
Table III E F P 6 0 , d e v i c e ~ 2 , d e t e r m i n a t i o n of
Sj~(f)/(V~ -
(Va - Vd) 3'2
Sl,(f)
50 75 100 125
0.354 0.650 1.00 1.40
2.60 x 4.30 × 6.10x 8.70 x
x x × ×
103 103 103 103
Table IV E F P 6 0 , d e v i c e ~¢2, d e t e r m i n a t i o n of V2(V )
S,a(f)
250 225 200 175
8.7 3.4 1.3 0.3
x x × x
10 -19 10 -19 10 -19 10 -19
Sla(f)/821a.
× x x x x
10 -17 10 -17 10 -17 10 -17 10 17 + 0 . 3 5 x 10 17
lid) 3/2. E x p e r i m e n t a l c o n d i t i o n s : f = 10 H z , I , = 8.0 m A , 3 = 3.1
(V~ - Vd)(V )
313
S,,(f)/(V~ - lid) 3'2 10 -19 10 -19 10 -19 10 -19
7.34 × 6.62 x 6.10x 6.21 x A v e . 6.57 x
10 -22 10 -22 10 22 10 -22 10 -22 _+ 0.41 x 10 z2
E x p e r i m e n t a l c o n d i t i o n s : f = 10 Hz, Va - Vd = 125 V
6
l,(mA)
3 21,(mA)
Sla(f)/621a
3.1 2.6 2.1 1.7
8.0 5.0 2.5 1.2
76.88 33.80 11.03 3.55
1.13 1.01 1.18 0.87 A v e . 1.05
× x x x ×
10 17 10 -17 10 -17 10 -17 . 10 -17 --- 0.12 × 10 -17
P. Fang and A. van der Ziel / Study of secondary emission 1/f noise
314 107 A#1:
Va,=125(V )
la= 8.OMA
5=3.1
•
V a, = 125 (V)
Ia = 10,0 M A
6 =
#2:
--
3.6
Average
10-16
O Devices #1 Z~ Devices #2
Va - Vd =125V Va - Vd =125V
106 0
10-17 rr
O A
z~
0 ,
O , , ~ , ~
Z~,,
105
10-18
I
I
10
102
103
821a (MA) n4 1"100
l
101
102
103
Fig. 3. S1a(f)/821 a versus 821~.
f (HZ)
EFP 60 Rns vs. f
Fig. 1. Secondary emission current 1/f noise spectra.
-{3"-'O--'O-
Devices #1
-II'--ll--II-
10-10
Devices #2
10 -20
O Devices #1 /k Devices #2 #1 la=10.OMA 8=3.6 #2 Ia = 8.0 M A ~ = 3.1 - Average
0
'
0
0
0
&
~
z3
10 20
10 -21
A
v
10-21
I
I
I
I
50
100
150
200
250
621AV 3/2 10"22
I
I
I
I
I
50
75
1O0
125
150
Fig.
4.
S&(f)/[(V,- Vd)3/Zla82]v e r s u s
(V,-
V~)3/Zla62.
175
(v) (Va - Vd)
Fig.
2. S&(f)/(V, - Vo)3'2
versus (Va - - Vd).
dependent of bias too, as shown in fig. 4. Taking the average for the two tubes we deduce an average secondary electron path length of 0.56 cm which is entirely reasonable and in good agreement with Van der Ziel's earlier estimate [2] of 0.50 cm. Hence the experiments are reliable, and the data verify eq. (1). In particular the ~ 2 term in (1) is essential; removing it would
give rise to a discrepancy between theory and experiment of a factor 10.
3. Analysis and conclusions The EFP60 secondary emission tubes are collision-free devices. Unless there are classical forms of 1 / f noise present, the only possible noise mechanism is electron accelaration between dynode and anode. Such classical noise mechanisms would be:
P. Fang and A. van der Ziel / Study of secondary emission 1/f noise a) Emission 1 / f noise fluctuations in the cathode current: they were removed by cathode feedback and hence do not concern us here. b) Fluctuations in secondary emission caused by fluctuations in the work function of the dynode. Since they are emission fluctuations, they should be independent of (Va - Vd), whereas our data show a ( V , - Vd) 3/2 dependence, hence this mechanism can be eliminated. c) In addition, we could have partition 1/f noise, which may or may not be of classical origin. However, it can be removed by cathode feedback as in (a) by h.f. connecting the screen grid to the cathode. Even if we did not apply partition 1 / f noise feedback, the experiments showed that partition 1 / f noise was much smaller than the secondary emission 1/f noise. What have we verified about eq. (1)? In the first place, we have verified the Av2/c 2 term; we shall see below that it comes from Bremsstrahlung. In the second place, we verified that the fine structure constant a 0 for electrons must be replaced by %6 2 for the charge conglomerates 6e associated with the secondary electrons. Apparently these charge conglomerates, which are generated within 10 -12 s, move through the tube as a unit; hence they also generate Bremsstrahlung as a unit (see below). Finally, the verification of the term 4a0/(3-rr ) follows from the overall numerical agreement between theory and experiment (dd, estimate). How can electron acceleration produce 1 / f noise? Because the acceleration produces Bremsstrahlung; according to Handel the energy spectrum S e ( f ) of the Bremsstrahlung is white, but the number spectrum S N ( f ) of the emitted quanta is equal to S e ( f ) / h f and hence varies as 1 / f [4]. Hence the current spectrum, which is a direct consequence of it, also varies as 1/f. According to the classical theory [5] of Bremsstrahlung generated by a single charge conglomerate q = ~e, the power P emitted by an accelerated conglomerate is: p ( t ) = 2qZ ( dv ] z 3C 3 \ d t / '
(6)
where dv/dt accelaration, transit time, Since P(t) is
is the acceleration. For constant
dv/dt = AvI~-, where 7 is the carrier and the radiated energy E = P(t)'c. constant for 0 < t < ~-,
E "2qz Av2 - 2 e 2 ( q ] Z ( A v 2 ] l 3C 3
r
315
(6a)
3c \ e / \ c 2 / ~"
Comparing this with eq. (1), we recognize the term AO2/C2 and the t e r m (q/e)2=~ 2, which follows directly from the fact that the carriers consist of charge conglomerates q = 6e. Finally, z corresponds to rda in eq. (1). The major part of eq. (1) thus follows directly from the Bremsstrahlung hypothesis, and may not be very sensitive to possible errors in Handel's derivation of the Hooge parameter a n [eq. (2b)]. Does the experimental verification of Handel's equation (2b) also justify Handel's derivation of it? Not necessarily. True, the Bremsstrahlung hypothesis seems to be correct; furthermore, eq. (1), and hence eq. (2b), seems to be correct. But the derivation in between is fully open to criticism, modification and improvement. Care should be taken, however, that eq. (2b) remains intact in these alterations, for it seems to be valid.
Acknowledgements This work was supported by A R O grant No. DAAG29-85-K-0235. We thank Dr. F.M. Klaassen, Philips Research Laboratories, for providing the EFP60 samples that made this work possible.
References [1] R.C. Schwantes and A. van der Ziel, Physica 26 (1960) 1162. [2] A. van der Ziel, Physica 144B (1987) 205. [3] F.N. Hooge, Phys. Lett. A 29 (1969) 139. [4] P.H. Handel, Phys. Rev. Lett. 34 (1975) 1492; Phys. Rev. 22 (1980) 745. [5] A. van der Ziel and G. Bosman, to be published.
STUDY OF S E C O N D A R Y EMISSION
1/f NOISE
P. F A N G and A. VAN D E R Z I E L Electrical Engineering Department, University of Minnesota, Minneapolis, MN 55455, USA Received 25 May 1987 Revised manuscript received 4 August 1987
The secondary emission 1/f noise observed by Schwantes and Van der Ziel has been investigated in more detail. The new experiments were prompted by Van der Ziel's application of Handel's theory to Schwantes's 1960 secondary emission noise data. To that end we measured the spectrum Sl~(f ) versus (Va - Va)3/2 at constant current I a and constant 8 and the noise spectrum versus I,/52 at constant voltage (V, - Va) both for a large resistance Re in the cathode lead. The results show good agreement with Handel's prediction, i.e. Handel's expression for the Hooge parameter a H is here verified. We finally discuss the meaning of these results and show that the Bremsstrahlung hypothesis can explain most of the data.
and daa is the distance from dynode to anode. Substituting all of these into (1), we can write:
1. Introduction
The experiments were made on Philips EFP60 secondary emission tubes. Secondary emission 1/f noise in this kind of tube was observed by Schwantes and Van der Ziel [1] in 1960, but the quantum 1 / f noise behavior could not be investigated, since Handel's theory was not yet developed. Recently Van der Ziel [2] formulated Handel's prediction for the value of the Hooge parameter a H for these tubes, derived the formula 4 a 0 82 ( Av2'~ eI~ 2 Sla(f) = ~ \ - - ~ - / f--~da = 4KTgnsgma
(1)
and showed that eq. (1) could explain the experimental data (see below). H e r e Sl~(f ) is the secondary emission 1/f noise current spectrum, a 0 is the fine structure constant for electrons, Av is the velocity change of the secondary electrons along the electron path from dynode to anode, I a is the anode current, g ~ = OIa/3Va is the transconductance, rda is the transit time from the dynode to the anode, and 3 is the secondary emission multiplication factor. In our case,
Sla ( f ) = const.Ia 62(Va - Vd)3'2 ,
where the (Va - V o ) 3/2 term corresponds to the Av 3 term; here dW z comes from the acceleration process operating on the secondary electron and Av comes from the transit time of the carriers. Therefore, one can expect that both Sly(f)~ ( V a - V d ) 3/2 at constant 8 and I a and Sla(f )/ (82Ia) at constant (Va - V d ) should be independent of bias. Before discussing the measurements, we investigate the background of eq. (1). The Hooge equation [3] Sla ( f )
12a
aH
- fNcu
(2)
defines the Hooge parameter a n both theoretically and experimentally; Neff = Iaz/e is the effective number of carriers. Substituting for Noff yields
ela Sj~(f) = a H f,rda
Av2= __2e(Va --Vd )
(lb)
(2a)
m
2dd~ 2daa ~'d~- (Av) -- (2e/m)(V a - V u ) 1/2
(la)
so that a H can be evaluated by measuring Sla(f); the transit time za~ can be estimated with an
0378-4363 / 87 / $03.50 t~ Elsevier Science Publishers B .V. (North-Holland Physics Publishing Division)
312
P. Fang and A. van der Ziel / Study of secondary emission 1/f noise
accuracy of +-(20-30)%, caused by the inaccuracy in dda. Next Handel's equation [4] is introduced as modified by Van der Ziel: 4a { AV2'~ 4% AV2 an = ~-~\--~-'] = -~-w 32 5C
(2b)
so that eq. (1) follows from eq. (2a) by substituting (2b) into (2a). Here a = %32 is the fine structure constant for charge conglomerates q = 6e and % = 1/137 is the fine structure constant for electrons. Eq. (2b) expresses the fact that, since the charge conglomerates = 6e move as a unit, they also generate Bremsstrahlung as a unit. The experimental value of a H is defined in eq. (2a), whereas the theoretical value of ~n is defined by eq. (2b). They are independent of each other, but since both go back to eq. (2), they deal with the same parameter. Hence a comparison between theory and experiment is both possible and meaningful.
tion 1 / f noise, respectively. The conductance gx was introduced so that the uncorrelated noise generated by the cathode is represented by an equivalent noise emf eg at the grid, a noise current generator gxeg between screen grid and dynode, and by a noise current generator 6g x between dynode and anode [1]. If we use the same bias circuit as above, except that now the screen grid is connected to the cathode for ac, we have: Rr,' = ( 1 +
g x ) 2Rnt + Rnp + (1 + gmpRc)2Rns , gmp
(4)
R~c= ( 1 + gmp gx ~2 / R .t + R n p
(5)
and, since we measured that R'.¢ = R.¢, it follows from (3) and (5) that Rnt =
(1 -t- ~rnp _ , ?R / nt "4- Rnp ;
this means gx/gmp and Rnp are negligible. Then (2) and (4) can be written: 2. Noise measurements
Rna = Rnt + (1 + gmtRc)2Rns The measurement configurations and the equivalent circuit can be found in ref. [1]. The principles of measurements in our experiments are the same as in ref. [1], and i.e. a large resistance Rc in the cathode lead provides feedback and so reduces the cathode 1 / f noise. If screen grid and dynode are both a.c. grounded we have for the noise resistance Rna and Rnc with feedback ena ____[1 + (gg___~_Xomp)(l+gmtec)]zRnt +(1 + gmtnc)2(Rn~ + R.p)
(3)
and R.c = R . , ,
(3a)
where R.¢ is measured at the cathode. Rnt, R,s, R.p are the noise resistances of the cathode 1 / f noise, secondary emission 1/f noise, and parti-
(screen grid connected to ground), 2 R~ = Rat + (1 + gmpRc) Rr,s (screen grid connected to cathode), R.s = (R.a - Rnt)/(1 + gmtR¢) 2 = ( R " - Rnt)/(1 + gmpRc) 2 . Using this method, Schwantes and Van der Ziel found that Rns at 10Hz was 0 . 4 6 M ~ , at the appropriate bias. Van der Ziel [2] found, in turn, that this result was in very good agreement with eq. (1), if he took for dda the plausible value of 0.50cm, but did not use any other adjustable parameters. The value of 0.50cm was chosen from early memory of the tube design and might be off by 20-30%. We first repeated the experiment under the same condition. Then we went one step further
P. Fang and A. van der Ziel / Study of secondary emission 1/f noise
to measure the functional dependence of the noise spectra on voltage, current and 6. In the experiments of S i . ( f ) versus (V~- Vo)3j2, we kept I~ and 6 constant and changed ( V ~ - lid) from 50 V to 125 V. Two devices were measured. Then we measured Sl~(f ) versus 82I, by keeping V~ - V a = 125 V and changing 6 and 1 by changing V2. The experimental conditions and results are shown in tables I-IV. To make sure that the secondary emission noise in our experiments had a 1/f noise spectrum, the spectra Sza(f ) versus Table I E F P 6 0 , d e v i c e # 1, d e t e r m i n a t i o n of
Sta(f)/(Va - lid) ~2.
frequency were measured. The results shown in fig. 1 give I / f noise. Figs. 2 - 4 give St~(f)/(V a )3/2, : Sl~(f)/(62ia) and S,.(f)/[(V aV~)3/26 I~], respectively for each of the two tubes. From the data we can clearly see that S~(f)/ (Va - Vd)3/2 and Sta(f)/(62Ia) are independent of bias within experimental error as the theory requires. Furthermore, we had evaluated Sl~(f ) / [(Va - Vd)3/2Ia 32] based on our data and can now conclude from this that for each tube it is in-
E x p e r i m e n t a l c o n d i t i o n s : f = 10 Hz, I~ = 10.0 m A , 8 = 3.6
( V a - Vd)(V )
(V, - I'd) 3/2
Sl~(f)(A2/nz)
Sla(f)/(V a Vd) 3/2
50 75 100 125
0.354 0.650 1.000 1.400
0.48 1.06 1.56 2.32
1.34 1.63 1.56 1.66 A v e . 1.55
x x x ×
103 103 103 103
Table II E F P 6 0 , d e v i c e ~ 1, d e t e r m i n a t i o n of
St~(f )/3 21,.
× x x ×
- -
10 -18 10 -18 10 -18 10 -18
× x × × ×
10 -21 10 Zl 10 zl 10 21 10 -21 -+ 0.09 x 10 -zl
E x p e r i m e n t a l c o n d i t i o n s : f = 10 Hz, V~ - V~ = 125 V
V2(V )
S~(f)(AZ/Hz)
3
la(mA)
82/~(mA)
Sta/6Zl.
250 225 200 175
2.3 9.4 2.7 1.5
3.60 3.04 2.43 1.97
10.00 5.88 2.94 1.44
129.60 54.30 17.40 5.88
1.77 1.73 1.56 2.60 A v e . 1.92
× × × ×
10 -13 10 -19 10 -19 10 -19
Table III E F P 6 0 , d e v i c e ~ 2 , d e t e r m i n a t i o n of
Sj~(f)/(V~ -
(Va - Vd) 3'2
Sl,(f)
50 75 100 125
0.354 0.650 1.00 1.40
2.60 x 4.30 × 6.10x 8.70 x
x x × ×
103 103 103 103
Table IV E F P 6 0 , d e v i c e ~¢2, d e t e r m i n a t i o n of V2(V )
S,a(f)
250 225 200 175
8.7 3.4 1.3 0.3
x x × x
10 -19 10 -19 10 -19 10 -19
Sla(f)/821a.
× x x x x
10 -17 10 -17 10 -17 10 -17 10 17 + 0 . 3 5 x 10 17
lid) 3/2. E x p e r i m e n t a l c o n d i t i o n s : f = 10 H z , I , = 8.0 m A , 3 = 3.1
(V~ - Vd)(V )
313
S,,(f)/(V~ - lid) 3'2 10 -19 10 -19 10 -19 10 -19
7.34 × 6.62 x 6.10x 6.21 x A v e . 6.57 x
10 -22 10 -22 10 22 10 -22 10 -22 _+ 0.41 x 10 z2
E x p e r i m e n t a l c o n d i t i o n s : f = 10 Hz, Va - Vd = 125 V
6
l,(mA)
3 21,(mA)
Sla(f)/621a
3.1 2.6 2.1 1.7
8.0 5.0 2.5 1.2
76.88 33.80 11.03 3.55
1.13 1.01 1.18 0.87 A v e . 1.05
× x x x ×
10 17 10 -17 10 -17 10 -17 . 10 -17 --- 0.12 × 10 -17
P. Fang and A. van der Ziel / Study of secondary emission 1/f noise
314 107 A#1:
Va,=125(V )
la= 8.OMA
5=3.1
•
V a, = 125 (V)
Ia = 10,0 M A
6 =
#2:
--
3.6
Average
10-16
O Devices #1 Z~ Devices #2
Va - Vd =125V Va - Vd =125V
106 0
10-17 rr
O A
z~
0 ,
O , , ~ , ~
Z~,,
105
10-18
I
I
10
102
103
821a (MA) n4 1"100
l
101
102
103
Fig. 3. S1a(f)/821 a versus 821~.
f (HZ)
EFP 60 Rns vs. f
Fig. 1. Secondary emission current 1/f noise spectra.
-{3"-'O--'O-
Devices #1
-II'--ll--II-
10-10
Devices #2
10 -20
O Devices #1 /k Devices #2 #1 la=10.OMA 8=3.6 #2 Ia = 8.0 M A ~ = 3.1 - Average
0
'
0
0
0
&
~
z3
10 20
10 -21
A
v
10-21
I
I
I
I
50
100
150
200
250
621AV 3/2 10"22
I
I
I
I
I
50
75
1O0
125
150
Fig.
4.
S&(f)/[(V,- Vd)3/Zla82]v e r s u s
(V,-
V~)3/Zla62.
175
(v) (Va - Vd)
Fig.
2. S&(f)/(V, - Vo)3'2
versus (Va - - Vd).
dependent of bias too, as shown in fig. 4. Taking the average for the two tubes we deduce an average secondary electron path length of 0.56 cm which is entirely reasonable and in good agreement with Van der Ziel's earlier estimate [2] of 0.50 cm. Hence the experiments are reliable, and the data verify eq. (1). In particular the ~ 2 term in (1) is essential; removing it would
give rise to a discrepancy between theory and experiment of a factor 10.
3. Analysis and conclusions The EFP60 secondary emission tubes are collision-free devices. Unless there are classical forms of 1 / f noise present, the only possible noise mechanism is electron accelaration between dynode and anode. Such classical noise mechanisms would be:
P. Fang and A. van der Ziel / Study of secondary emission 1/f noise a) Emission 1 / f noise fluctuations in the cathode current: they were removed by cathode feedback and hence do not concern us here. b) Fluctuations in secondary emission caused by fluctuations in the work function of the dynode. Since they are emission fluctuations, they should be independent of (Va - Vd), whereas our data show a ( V , - Vd) 3/2 dependence, hence this mechanism can be eliminated. c) In addition, we could have partition 1/f noise, which may or may not be of classical origin. However, it can be removed by cathode feedback as in (a) by h.f. connecting the screen grid to the cathode. Even if we did not apply partition 1 / f noise feedback, the experiments showed that partition 1 / f noise was much smaller than the secondary emission 1/f noise. What have we verified about eq. (1)? In the first place, we have verified the Av2/c 2 term; we shall see below that it comes from Bremsstrahlung. In the second place, we verified that the fine structure constant a 0 for electrons must be replaced by %6 2 for the charge conglomerates 6e associated with the secondary electrons. Apparently these charge conglomerates, which are generated within 10 -12 s, move through the tube as a unit; hence they also generate Bremsstrahlung as a unit (see below). Finally, the verification of the term 4a0/(3-rr ) follows from the overall numerical agreement between theory and experiment (dd, estimate). How can electron acceleration produce 1 / f noise? Because the acceleration produces Bremsstrahlung; according to Handel the energy spectrum S e ( f ) of the Bremsstrahlung is white, but the number spectrum S N ( f ) of the emitted quanta is equal to S e ( f ) / h f and hence varies as 1 / f [4]. Hence the current spectrum, which is a direct consequence of it, also varies as 1/f. According to the classical theory [5] of Bremsstrahlung generated by a single charge conglomerate q = ~e, the power P emitted by an accelerated conglomerate is: p ( t ) = 2qZ ( dv ] z 3C 3 \ d t / '
(6)
where dv/dt accelaration, transit time, Since P(t) is
is the acceleration. For constant
dv/dt = AvI~-, where 7 is the carrier and the radiated energy E = P(t)'c. constant for 0 < t < ~-,
E "2qz Av2 - 2 e 2 ( q ] Z ( A v 2 ] l 3C 3
r
315
(6a)
3c \ e / \ c 2 / ~"
Comparing this with eq. (1), we recognize the term AO2/C2 and the t e r m (q/e)2=~ 2, which follows directly from the fact that the carriers consist of charge conglomerates q = 6e. Finally, z corresponds to rda in eq. (1). The major part of eq. (1) thus follows directly from the Bremsstrahlung hypothesis, and may not be very sensitive to possible errors in Handel's derivation of the Hooge parameter a n [eq. (2b)]. Does the experimental verification of Handel's equation (2b) also justify Handel's derivation of it? Not necessarily. True, the Bremsstrahlung hypothesis seems to be correct; furthermore, eq. (1), and hence eq. (2b), seems to be correct. But the derivation in between is fully open to criticism, modification and improvement. Care should be taken, however, that eq. (2b) remains intact in these alterations, for it seems to be valid.
Acknowledgements This work was supported by A R O grant No. DAAG29-85-K-0235. We thank Dr. F.M. Klaassen, Philips Research Laboratories, for providing the EFP60 samples that made this work possible.
References [1] R.C. Schwantes and A. van der Ziel, Physica 26 (1960) 1162. [2] A. van der Ziel, Physica 144B (1987) 205. [3] F.N. Hooge, Phys. Lett. A 29 (1969) 139. [4] P.H. Handel, Phys. Rev. Lett. 34 (1975) 1492; Phys. Rev. 22 (1980) 745. [5] A. van der Ziel and G. Bosman, to be published.